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+/****************************************************************************
+ *
+ * ftcalc.h
+ *
+ * Arithmetic computations (specification).
+ *
+ * Copyright (C) 1996-2023 by
+ * David Turner, Robert Wilhelm, and Werner Lemberg.
+ *
+ * This file is part of the FreeType project, and may only be used,
+ * modified, and distributed under the terms of the FreeType project
+ * license, LICENSE.TXT. By continuing to use, modify, or distribute
+ * this file you indicate that you have read the license and
+ * understand and accept it fully.
+ *
+ */
+
+
+#ifndef FTCALC_H_
+#define FTCALC_H_
+
+
+#include <freetype/freetype.h>
+
+#include "compiler-macros.h"
+
+FT_BEGIN_HEADER
+
+
+ /**************************************************************************
+ *
+ * FT_MulDiv() and FT_MulFix() are declared in freetype.h.
+ *
+ */
+
+#ifndef FT_CONFIG_OPTION_NO_ASSEMBLER
+ /* Provide assembler fragments for performance-critical functions. */
+ /* These must be defined `static __inline__' with GCC. */
+
+#if defined( __CC_ARM ) || defined( __ARMCC__ ) /* RVCT */
+
+#define FT_MULFIX_ASSEMBLER FT_MulFix_arm
+
+ /* documentation is in freetype.h */
+
+ static __inline FT_Int32
+ FT_MulFix_arm( FT_Int32 a,
+ FT_Int32 b )
+ {
+ FT_Int32 t, t2;
+
+
+ __asm
+ {
+ smull t2, t, b, a /* (lo=t2,hi=t) = a*b */
+ mov a, t, asr #31 /* a = (hi >> 31) */
+ add a, a, #0x8000 /* a += 0x8000 */
+ adds t2, t2, a /* t2 += a */
+ adc t, t, #0 /* t += carry */
+ mov a, t2, lsr #16 /* a = t2 >> 16 */
+ orr a, a, t, lsl #16 /* a |= t << 16 */
+ }
+ return a;
+ }
+
+#endif /* __CC_ARM || __ARMCC__ */
+
+
+#ifdef __GNUC__
+
+#if defined( __arm__ ) && \
+ ( !defined( __thumb__ ) || defined( __thumb2__ ) ) && \
+ !( defined( __CC_ARM ) || defined( __ARMCC__ ) )
+
+#define FT_MULFIX_ASSEMBLER FT_MulFix_arm
+
+ /* documentation is in freetype.h */
+
+ static __inline__ FT_Int32
+ FT_MulFix_arm( FT_Int32 a,
+ FT_Int32 b )
+ {
+ FT_Int32 t, t2;
+
+
+ __asm__ __volatile__ (
+ "smull %1, %2, %4, %3\n\t" /* (lo=%1,hi=%2) = a*b */
+ "mov %0, %2, asr #31\n\t" /* %0 = (hi >> 31) */
+#if defined( __clang__ ) && defined( __thumb2__ )
+ "add.w %0, %0, #0x8000\n\t" /* %0 += 0x8000 */
+#else
+ "add %0, %0, #0x8000\n\t" /* %0 += 0x8000 */
+#endif
+ "adds %1, %1, %0\n\t" /* %1 += %0 */
+ "adc %2, %2, #0\n\t" /* %2 += carry */
+ "mov %0, %1, lsr #16\n\t" /* %0 = %1 >> 16 */
+ "orr %0, %0, %2, lsl #16\n\t" /* %0 |= %2 << 16 */
+ : "=r"(a), "=&r"(t2), "=&r"(t)
+ : "r"(a), "r"(b)
+ : "cc" );
+ return a;
+ }
+
+#endif /* __arm__ && */
+ /* ( __thumb2__ || !__thumb__ ) && */
+ /* !( __CC_ARM || __ARMCC__ ) */
+
+
+#if defined( __i386__ )
+
+#define FT_MULFIX_ASSEMBLER FT_MulFix_i386
+
+ /* documentation is in freetype.h */
+
+ static __inline__ FT_Int32
+ FT_MulFix_i386( FT_Int32 a,
+ FT_Int32 b )
+ {
+ FT_Int32 result;
+
+
+ __asm__ __volatile__ (
+ "imul %%edx\n"
+ "movl %%edx, %%ecx\n"
+ "sarl $31, %%ecx\n"
+ "addl $0x8000, %%ecx\n"
+ "addl %%ecx, %%eax\n"
+ "adcl $0, %%edx\n"
+ "shrl $16, %%eax\n"
+ "shll $16, %%edx\n"
+ "addl %%edx, %%eax\n"
+ : "=a"(result), "=d"(b)
+ : "a"(a), "d"(b)
+ : "%ecx", "cc" );
+ return result;
+ }
+
+#endif /* i386 */
+
+#endif /* __GNUC__ */
+
+
+#ifdef _MSC_VER /* Visual C++ */
+
+#ifdef _M_IX86
+
+#define FT_MULFIX_ASSEMBLER FT_MulFix_i386
+
+ /* documentation is in freetype.h */
+
+ static __inline FT_Int32
+ FT_MulFix_i386( FT_Int32 a,
+ FT_Int32 b )
+ {
+ FT_Int32 result;
+
+ __asm
+ {
+ mov eax, a
+ mov edx, b
+ imul edx
+ mov ecx, edx
+ sar ecx, 31
+ add ecx, 8000h
+ add eax, ecx
+ adc edx, 0
+ shr eax, 16
+ shl edx, 16
+ add eax, edx
+ mov result, eax
+ }
+ return result;
+ }
+
+#endif /* _M_IX86 */
+
+#endif /* _MSC_VER */
+
+
+#if defined( __GNUC__ ) && defined( __x86_64__ )
+
+#define FT_MULFIX_ASSEMBLER FT_MulFix_x86_64
+
+ static __inline__ FT_Int32
+ FT_MulFix_x86_64( FT_Int32 a,
+ FT_Int32 b )
+ {
+ /* Temporarily disable the warning that C90 doesn't support */
+ /* `long long'. */
+#if __GNUC__ > 4 || ( __GNUC__ == 4 && __GNUC_MINOR__ >= 6 )
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wlong-long"
+#endif
+
+#if 1
+ /* Technically not an assembly fragment, but GCC does a really good */
+ /* job at inlining it and generating good machine code for it. */
+ long long ret, tmp;
+
+
+ ret = (long long)a * b;
+ tmp = ret >> 63;
+ ret += 0x8000 + tmp;
+
+ return (FT_Int32)( ret >> 16 );
+#else
+
+ /* For some reason, GCC 4.6 on Ubuntu 12.04 generates invalid machine */
+ /* code from the lines below. The main issue is that `wide_a' is not */
+ /* properly initialized by sign-extending `a'. Instead, the generated */
+ /* machine code assumes that the register that contains `a' on input */
+ /* can be used directly as a 64-bit value, which is wrong most of the */
+ /* time. */
+ long long wide_a = (long long)a;
+ long long wide_b = (long long)b;
+ long long result;
+
+
+ __asm__ __volatile__ (
+ "imul %2, %1\n"
+ "mov %1, %0\n"
+ "sar $63, %0\n"
+ "lea 0x8000(%1, %0), %0\n"
+ "sar $16, %0\n"
+ : "=&r"(result), "=&r"(wide_a)
+ : "r"(wide_b)
+ : "cc" );
+
+ return (FT_Int32)result;
+#endif
+
+#if __GNUC__ > 4 || ( __GNUC__ == 4 && __GNUC_MINOR__ >= 6 )
+#pragma GCC diagnostic pop
+#endif
+ }
+
+#endif /* __GNUC__ && __x86_64__ */
+
+#endif /* !FT_CONFIG_OPTION_NO_ASSEMBLER */
+
+
+#ifdef FT_CONFIG_OPTION_INLINE_MULFIX
+#ifdef FT_MULFIX_ASSEMBLER
+#define FT_MulFix( a, b ) FT_MULFIX_ASSEMBLER( (FT_Int32)(a), (FT_Int32)(b) )
+#endif
+#endif
+
+
+ /**************************************************************************
+ *
+ * @function:
+ * FT_MulDiv_No_Round
+ *
+ * @description:
+ * A very simple function used to perform the computation '(a*b)/c'
+ * (without rounding) with maximum accuracy (it uses a 64-bit
+ * intermediate integer whenever necessary).
+ *
+ * This function isn't necessarily as fast as some processor-specific
+ * operations, but is at least completely portable.
+ *
+ * @input:
+ * a ::
+ * The first multiplier.
+ * b ::
+ * The second multiplier.
+ * c ::
+ * The divisor.
+ *
+ * @return:
+ * The result of '(a*b)/c'. This function never traps when trying to
+ * divide by zero; it simply returns 'MaxInt' or 'MinInt' depending on
+ * the signs of 'a' and 'b'.
+ */
+ FT_BASE( FT_Long )
+ FT_MulDiv_No_Round( FT_Long a,
+ FT_Long b,
+ FT_Long c );
+
+
+ /**************************************************************************
+ *
+ * @function:
+ * FT_MulAddFix
+ *
+ * @description:
+ * Compute `(s[0] * f[0] + s[1] * f[1] + ...) / 0x10000`, where `s[n]` is
+ * usually a 16.16 scalar.
+ *
+ * @input:
+ * s ::
+ * The array of scalars.
+ * f ::
+ * The array of factors.
+ * count ::
+ * The number of entries in the array.
+ *
+ * @return:
+ * The result of `(s[0] * f[0] + s[1] * f[1] + ...) / 0x10000`.
+ *
+ * @note:
+ * This function is currently used for the scaled delta computation of
+ * variation stores. It internally uses 64-bit data types when
+ * available, otherwise it emulates 64-bit math by using 32-bit
+ * operations, which produce a correct result but most likely at a slower
+ * performance in comparison to the implementation base on `int64_t`.
+ *
+ */
+ FT_BASE( FT_Int32 )
+ FT_MulAddFix( FT_Fixed* s,
+ FT_Int32* f,
+ FT_UInt count );
+
+
+ /*
+ * A variant of FT_Matrix_Multiply which scales its result afterwards. The
+ * idea is that both `a' and `b' are scaled by factors of 10 so that the
+ * values are as precise as possible to get a correct result during the
+ * 64bit multiplication. Let `sa' and `sb' be the scaling factors of `a'
+ * and `b', respectively, then the scaling factor of the result is `sa*sb'.
+ */
+ FT_BASE( void )
+ FT_Matrix_Multiply_Scaled( const FT_Matrix* a,
+ FT_Matrix *b,
+ FT_Long scaling );
+
+
+ /*
+ * Check a matrix. If the transformation would lead to extreme shear or
+ * extreme scaling, for example, return 0. If everything is OK, return 1.
+ *
+ * Based on geometric considerations we use the following inequality to
+ * identify a degenerate matrix.
+ *
+ * 50 * abs(xx*yy - xy*yx) < xx^2 + xy^2 + yx^2 + yy^2
+ *
+ * Value 50 is heuristic.
+ */
+ FT_BASE( FT_Bool )
+ FT_Matrix_Check( const FT_Matrix* matrix );
+
+
+ /*
+ * A variant of FT_Vector_Transform. See comments for
+ * FT_Matrix_Multiply_Scaled.
+ */
+ FT_BASE( void )
+ FT_Vector_Transform_Scaled( FT_Vector* vector,
+ const FT_Matrix* matrix,
+ FT_Long scaling );
+
+
+ /*
+ * This function normalizes a vector and returns its original length. The
+ * normalized vector is a 16.16 fixed-point unit vector with length close
+ * to 0x10000. The accuracy of the returned length is limited to 16 bits
+ * also. The function utilizes quick inverse square root approximation
+ * without divisions and square roots relying on Newton's iterations
+ * instead.
+ */
+ FT_BASE( FT_UInt32 )
+ FT_Vector_NormLen( FT_Vector* vector );
+
+
+ /*
+ * Return -1, 0, or +1, depending on the orientation of a given corner. We
+ * use the Cartesian coordinate system, with positive vertical values going
+ * upwards. The function returns +1 if the corner turns to the left, -1 to
+ * the right, and 0 for undecidable cases.
+ */
+ FT_BASE( FT_Int )
+ ft_corner_orientation( FT_Pos in_x,
+ FT_Pos in_y,
+ FT_Pos out_x,
+ FT_Pos out_y );
+
+
+ /*
+ * Return TRUE if a corner is flat or nearly flat. This is equivalent to
+ * saying that the corner point is close to its neighbors, or inside an
+ * ellipse defined by the neighbor focal points to be more precise.
+ */
+ FT_BASE( FT_Int )
+ ft_corner_is_flat( FT_Pos in_x,
+ FT_Pos in_y,
+ FT_Pos out_x,
+ FT_Pos out_y );
+
+
+ /*
+ * Return the most significant bit index.
+ */
+
+#ifndef FT_CONFIG_OPTION_NO_ASSEMBLER
+
+#if defined( __clang__ ) || ( defined( __GNUC__ ) && \
+ ( __GNUC__ > 3 || ( __GNUC__ == 3 && __GNUC_MINOR__ >= 4 ) ) )
+
+#if FT_SIZEOF_INT == 4
+
+#define FT_MSB( x ) ( 31 - __builtin_clz( x ) )
+
+#elif FT_SIZEOF_LONG == 4
+
+#define FT_MSB( x ) ( 31 - __builtin_clzl( x ) )
+
+#endif
+
+#elif defined( _MSC_VER ) && _MSC_VER >= 1400
+
+#if defined( _WIN32_WCE )
+
+#include <cmnintrin.h>
+#pragma intrinsic( _CountLeadingZeros )
+
+#define FT_MSB( x ) ( 31 - _CountLeadingZeros( x ) )
+
+#elif defined( _M_ARM64 ) || defined( _M_ARM )
+
+#include <intrin.h>
+#pragma intrinsic( _CountLeadingZeros )
+
+#define FT_MSB( x ) ( 31 - _CountLeadingZeros( x ) )
+
+#elif defined( _M_IX86 ) || defined( _M_AMD64 ) || defined( _M_IA64 )
+
+#include <intrin.h>
+#pragma intrinsic( _BitScanReverse )
+
+ static __inline FT_Int32
+ FT_MSB_i386( FT_UInt32 x )
+ {
+ unsigned long where;
+
+
+ _BitScanReverse( &where, x );
+
+ return (FT_Int32)where;
+ }
+
+#define FT_MSB( x ) FT_MSB_i386( x )
+
+#endif
+
+#elif defined( __WATCOMC__ ) && defined( __386__ )
+
+ extern __inline FT_Int32
+ FT_MSB_i386( FT_UInt32 x );
+
+#pragma aux FT_MSB_i386 = \
+ "bsr eax, eax" \
+ __parm [__eax] __nomemory \
+ __value [__eax] \
+ __modify __exact [__eax] __nomemory;
+
+#define FT_MSB( x ) FT_MSB_i386( x )
+
+#elif defined( __DECC ) || defined( __DECCXX )
+
+#include <builtins.h>
+
+#define FT_MSB( x ) (FT_Int)( 63 - _leadz( x ) )
+
+#elif defined( _CRAYC )
+
+#include <intrinsics.h>
+
+#define FT_MSB( x ) (FT_Int)( 31 - _leadz32( x ) )
+
+#endif /* FT_MSB macro definitions */
+
+#endif /* !FT_CONFIG_OPTION_NO_ASSEMBLER */
+
+
+#ifndef FT_MSB
+
+ FT_BASE( FT_Int )
+ FT_MSB( FT_UInt32 z );
+
+#endif
+
+
+ /*
+ * Return sqrt(x*x+y*y), which is the same as `FT_Vector_Length' but uses
+ * two fixed-point arguments instead.
+ */
+ FT_BASE( FT_Fixed )
+ FT_Hypot( FT_Fixed x,
+ FT_Fixed y );
+
+
+#if 0
+
+ /**************************************************************************
+ *
+ * @function:
+ * FT_SqrtFixed
+ *
+ * @description:
+ * Computes the square root of a 16.16 fixed-point value.
+ *
+ * @input:
+ * x ::
+ * The value to compute the root for.
+ *
+ * @return:
+ * The result of 'sqrt(x)'.
+ *
+ * @note:
+ * This function is not very fast.
+ */
+ FT_BASE( FT_Int32 )
+ FT_SqrtFixed( FT_Int32 x );
+
+#endif /* 0 */
+
+
+#define INT_TO_F26DOT6( x ) ( (FT_Long)(x) * 64 ) /* << 6 */
+#define INT_TO_F2DOT14( x ) ( (FT_Long)(x) * 16384 ) /* << 14 */
+#define INT_TO_FIXED( x ) ( (FT_Long)(x) * 65536 ) /* << 16 */
+#define F2DOT14_TO_FIXED( x ) ( (FT_Long)(x) * 4 ) /* << 2 */
+#define FIXED_TO_INT( x ) ( FT_RoundFix( x ) >> 16 )
+
+#define ROUND_F26DOT6( x ) ( ( (x) + 32 - ( x < 0 ) ) & -64 )
+
+ /*
+ * The following macros have two purposes.
+ *
+ * - Tag places where overflow is expected and harmless.
+ *
+ * - Avoid run-time sanitizer errors.
+ *
+ * Use with care!
+ */
+#define ADD_INT( a, b ) \
+ (FT_Int)( (FT_UInt)(a) + (FT_UInt)(b) )
+#define SUB_INT( a, b ) \
+ (FT_Int)( (FT_UInt)(a) - (FT_UInt)(b) )
+#define MUL_INT( a, b ) \
+ (FT_Int)( (FT_UInt)(a) * (FT_UInt)(b) )
+#define NEG_INT( a ) \
+ (FT_Int)( (FT_UInt)0 - (FT_UInt)(a) )
+
+#define ADD_LONG( a, b ) \
+ (FT_Long)( (FT_ULong)(a) + (FT_ULong)(b) )
+#define SUB_LONG( a, b ) \
+ (FT_Long)( (FT_ULong)(a) - (FT_ULong)(b) )
+#define MUL_LONG( a, b ) \
+ (FT_Long)( (FT_ULong)(a) * (FT_ULong)(b) )
+#define NEG_LONG( a ) \
+ (FT_Long)( (FT_ULong)0 - (FT_ULong)(a) )
+
+#define ADD_INT32( a, b ) \
+ (FT_Int32)( (FT_UInt32)(a) + (FT_UInt32)(b) )
+#define SUB_INT32( a, b ) \
+ (FT_Int32)( (FT_UInt32)(a) - (FT_UInt32)(b) )
+#define MUL_INT32( a, b ) \
+ (FT_Int32)( (FT_UInt32)(a) * (FT_UInt32)(b) )
+#define NEG_INT32( a ) \
+ (FT_Int32)( (FT_UInt32)0 - (FT_UInt32)(a) )
+
+#ifdef FT_INT64
+
+#define ADD_INT64( a, b ) \
+ (FT_Int64)( (FT_UInt64)(a) + (FT_UInt64)(b) )
+#define SUB_INT64( a, b ) \
+ (FT_Int64)( (FT_UInt64)(a) - (FT_UInt64)(b) )
+#define MUL_INT64( a, b ) \
+ (FT_Int64)( (FT_UInt64)(a) * (FT_UInt64)(b) )
+#define NEG_INT64( a ) \
+ (FT_Int64)( (FT_UInt64)0 - (FT_UInt64)(a) )
+
+#endif /* FT_INT64 */
+
+
+FT_END_HEADER
+
+#endif /* FTCALC_H_ */
+
+
+/* END */
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